On the minimal solution property of neutral functional-differential inclusion
type: Item
instance of: scholarly article
title: On the minimal solution property of neutral functional-differential inclusion
zbMATH Open document ID: 0729.34011
DOI: 10.1016/0022-247X(91)90135-M
author: Jerzy Motyl
published in: Journal of Mathematical Analysis and Applications
publication date: 1991-01-01T00:00:00Z
review text: Given a set-valued function \({\mathcal F}\) from \(L^ 1[a,b]\) into subsets of \(L^ 1[a,b]\) the initial-value problem \(\dot x\in {\mathcal F}(x)\), \(x(a)=x_ 0\), is considered. It is proved that if \({\mathcal F}\) is in any sense integral dissipative then a derivative function \(\dot x\) of a solution of the above functional inclusion is a minimal selector for \({\mathcal F}(x)\), i.e., such that \(\| \dot x\| =\min \{\| x\|:\) \(y\in {\mathcal F}(x)\}\). As a corollary of this result a similar theorem for neutral functional-differential inclusions of the form \(\dot x(t)\in F(t,x_ t,\dot x_ t)\) with a real set-valued function F is also obtained.
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34K40
zbMATH DE Number: 4204820
zbMATH Keywords: minimal-norm selection
zbMATH Keywords: multifunctions
zbMATH Keywords: initial-value problem
zbMATH Keywords: minimal selector
zbMATH Keywords: neutral functional-differential inclusions
reviewed by: Michał Kisielewicz
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4204820